LMFDB - Embedded newform 845.2.b.c.339.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(339,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.339"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-10,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.1
Root			$0.403032 - 0.403032i$ of defining polynomial
Character	$\chi$	$=$	845.339
Dual form			845.2.b.c.339.6

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.67513i q^{2} +0.481194i q^{3} -5.15633 q^{4} +(-1.67513 + 1.48119i) q^{5} +1.28726 q^{6} -0.806063i q^{7} +8.44358i q^{8} +2.76845 q^{9} +(3.96239 + 4.48119i) q^{10} +3.67513 q^{11} -2.48119i q^{12} -2.15633 q^{14} +(-0.712742 - 0.806063i) q^{15} +12.2750 q^{16} -1.35026i q^{17} -7.40597i q^{18} -1.67513 q^{19} +(8.63752 - 7.63752i) q^{20} +0.387873 q^{21} -9.83146i q^{22} -6.48119i q^{23} -4.06300 q^{24} +(0.612127 - 4.96239i) q^{25} +2.77575i q^{27} +4.15633i q^{28} -2.41819 q^{29} +(-2.15633 + 1.90668i) q^{30} +5.28726 q^{31} -15.9502i q^{32} +1.76845i q^{33} -3.61213 q^{34} +(1.19394 + 1.35026i) q^{35} -14.2750 q^{36} -3.76845i q^{37} +4.48119i q^{38} +(-12.5066 - 14.1441i) q^{40} +8.31265 q^{41} -1.03761i q^{42} +6.79384i q^{43} -18.9502 q^{44} +(-4.63752 + 4.10062i) q^{45} -17.3380 q^{46} -3.19394i q^{47} +5.90668i q^{48} +6.35026 q^{49} +(-13.2750 - 1.63752i) q^{50} +0.649738 q^{51} -5.73813i q^{53} +7.42548 q^{54} +(-6.15633 + 5.44358i) q^{55} +6.80606 q^{56} -0.806063i q^{57} +6.46898i q^{58} +5.98778 q^{59} +(3.67513 + 4.15633i) q^{60} -1.76845 q^{61} -14.1441i q^{62} -2.23155i q^{63} -18.1187 q^{64} +4.73084 q^{66} -9.89446i q^{67} +6.96239i q^{68} +3.11871 q^{69} +(3.61213 - 3.19394i) q^{70} -8.56230 q^{71} +23.3757i q^{72} -11.7685i q^{73} -10.0811 q^{74} +(2.38787 + 0.294552i) q^{75} +8.63752 q^{76} -2.96239i q^{77} +2.26187 q^{79} +(-20.5623 + 18.1817i) q^{80} +6.96968 q^{81} -22.2374i q^{82} +3.84367i q^{83} -2.00000 q^{84} +(2.00000 + 2.26187i) q^{85} +18.1744 q^{86} -1.16362i q^{87} +31.0313i q^{88} +2.77575 q^{89} +(10.9697 + 12.4060i) q^{90} +33.4191i q^{92} +2.54420i q^{93} -8.54420 q^{94} +(2.80606 - 2.48119i) q^{95} +7.67513 q^{96} +1.87399i q^{97} -16.9878i q^{98} +10.1744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} - 4 q^{6} - 6 q^{9} + 2 q^{10} + 12 q^{11} + 8 q^{14} - 16 q^{15} + 10 q^{16} + 20 q^{20} + 4 q^{21} - 16 q^{24} + 2 q^{25} - 12 q^{29} + 8 q^{30} + 20 q^{31} - 20 q^{34} + 8 q^{35} - 22 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) $ 6 * q - 10 * q^4 - 4 * q^6 - 6 * q^9 + 2 * q^10 + 12 * q^11 + 8 * q^14 - 16 * q^15 + 10 * q^16 + 20 * q^20 + 4 * q^21 - 16 * q^24 + 2 * q^25 - 12 * q^29 + 8 * q^30 + 20 * q^31 - 20 * q^34 + 8 * q^35 - 22 * q^36 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 4 * q^45 - 32 * q^46 + 18 * q^49 - 16 * q^50 + 24 * q^51 + 68 * q^54 - 16 * q^55 + 40 * q^56 - 16 * q^59 + 12 * q^60 + 12 * q^61 - 66 * q^64 - 16 * q^66 - 24 * q^69 + 20 * q^70 + 24 * q^71 + 4 * q^74 + 16 * q^75 + 20 * q^76 + 32 * q^79 - 48 * q^80 + 46 * q^81 - 12 * q^84 + 12 * q^85 + 32 * q^86 + 20 * q^89 + 70 * q^90 - 32 * q^94 + 16 * q^95 + 36 * q^96 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	2.67513i		−	1.89160i	−0.324745	−	0.945802i	$-0.605279\pi$
$2$		−	2.67513i		−	1.89160i	0.324745	−	0.945802i	$-0.394721\pi$
$3$			0.481194i			0.277818i	0.990305	+	0.138909i	$0.0443595\pi$
$3$			0.481194i			0.277818i	−0.990305	+	0.138909i	$0.955641\pi$
$4$	−5.15633			−2.57816
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$5$	−1.67513	+	1.48119i	−0.749141	+	0.662410i
$6$	1.28726			0.525521
$7$		−	0.806063i		−	0.304663i	−0.988329	−	0.152332i	$-0.951322\pi$
$7$		−	0.806063i		−	0.304663i	0.988329	−	0.152332i	$-0.0486782\pi$
$8$			8.44358i			2.98526i
$9$	2.76845			0.922817
$10$	3.96239	+	4.48119i	1.25302	+	1.41708i
$11$	3.67513			1.10809			0.554047	−	0.832486i	$-0.313083\pi$
$11$	3.67513			1.10809			0.554047	+	0.832486i	$0.313083\pi$
$12$		−	2.48119i		−	0.716259i
$13$		0			0
$13$		0			0
$14$	−2.15633			−0.576302
$15$	−0.712742	−	0.806063i	−0.184029	−	0.208125i
$16$	12.2750			3.06876
$17$		−	1.35026i		−	0.327487i	−0.986503	−	0.163743i	$-0.947643\pi$
$17$		−	1.35026i		−	0.327487i	0.986503	−	0.163743i	$-0.0523569\pi$
$18$		−	7.40597i		−	1.74560i
$19$	−1.67513			−0.384301			−0.192151	−	0.981365i	$-0.561546\pi$
$19$	−1.67513			−0.384301			−0.192151	+	0.981365i	$0.561546\pi$
$20$	8.63752	−	7.63752i	1.93141	−	1.70780i
$21$	0.387873			0.0846409
$22$		−	9.83146i		−	2.09607i
$23$		−	6.48119i		−	1.35142i	−0.737166	−	0.675711i	$-0.763837\pi$
$23$		−	6.48119i		−	1.35142i	0.737166	−	0.675711i	$-0.236163\pi$
$24$	−4.06300			−0.829357
$25$	0.612127	−	4.96239i	0.122425	−	0.992478i
$26$		0			0
$27$			2.77575i			0.534193i
$28$			4.15633i			0.785472i
$29$	−2.41819			−0.449047			−0.224523	−	0.974469i	$-0.572083\pi$
$29$	−2.41819			−0.449047			−0.224523	+	0.974469i	$0.572083\pi$
$30$	−2.15633	+	1.90668i	−0.393689	+	0.348110i
$31$	5.28726			0.949620			0.474810	−	0.880088i	$-0.342517\pi$
$31$	5.28726			0.949620			0.474810	+	0.880088i	$0.342517\pi$
$32$		−	15.9502i		−	2.81962i
$33$			1.76845i			0.307848i
$34$	−3.61213			−0.619475
$35$	1.19394	+	1.35026i	0.201812	+	0.228236i
$36$	−14.2750			−2.37917
$37$		−	3.76845i		−	0.619530i	−0.950813	−	0.309765i	$-0.899750\pi$
$37$		−	3.76845i		−	0.619530i	0.950813	−	0.309765i	$-0.100250\pi$
$38$			4.48119i			0.726946i
$39$		0			0
$40$	−12.5066	−	14.1441i	−1.97747	−	2.23638i
$41$	8.31265			1.29822			0.649109	−	0.760695i	$-0.275142\pi$
$41$	8.31265			1.29822			0.649109	+	0.760695i	$0.275142\pi$
$42$		−	1.03761i		−	0.160107i
$43$			6.79384i			1.03605i	0.855365	+	0.518026i	$0.173333\pi$
$43$			6.79384i			1.03605i	−0.855365	+	0.518026i	$0.826667\pi$
$44$	−18.9502			−2.85685
$45$	−4.63752	+	4.10062i	−0.691321	+	0.611284i
$46$	−17.3380			−2.55635
$47$		−	3.19394i		−	0.465884i	−0.972491	−	0.232942i	$-0.925165\pi$
$47$		−	3.19394i		−	0.465884i	0.972491	−	0.232942i	$-0.0748352\pi$
$48$			5.90668i			0.852556i
$49$	6.35026			0.907180
$50$	−13.2750	−	1.63752i	−1.87737	−	0.231580i
$51$	0.649738			0.0909816
$52$		0			0
$53$		−	5.73813i		−	0.788193i	−0.919069	−	0.394097i	$-0.871057\pi$
$53$		−	5.73813i		−	0.788193i	0.919069	−	0.394097i	$-0.128943\pi$
$54$	7.42548			1.01048
$55$	−6.15633	+	5.44358i	−0.830119	+	0.734013i
$56$	6.80606			0.909498
$57$		−	0.806063i		−	0.106766i
$58$			6.46898i			0.849418i
$59$	5.98778			0.779543			0.389771	−	0.920912i	$-0.372554\pi$
$59$	5.98778			0.779543			0.389771	+	0.920912i	$0.372554\pi$
$60$	3.67513	+	4.15633i	0.474457	+	0.536579i
$61$	−1.76845			−0.226427			−0.113214	−	0.993571i	$-0.536114\pi$
$61$	−1.76845			−0.226427			−0.113214	+	0.993571i	$0.536114\pi$
$62$		−	14.1441i		−	1.79630i
$63$		−	2.23155i		−	0.281149i
$64$	−18.1187			−2.26484
$65$		0			0
$66$	4.73084			0.582326
$67$		−	9.89446i		−	1.20880i	−0.796681	−	0.604400i	$-0.793413\pi$
$67$		−	9.89446i		−	1.20880i	0.796681	−	0.604400i	$-0.206587\pi$
$68$			6.96239i			0.844314i
$69$	3.11871			0.375449
$70$	3.61213	−	3.19394i	0.431732	−	0.381748i
$71$	−8.56230			−1.01616			−0.508079	−	0.861311i	$-0.669644\pi$
$71$	−8.56230			−1.01616			−0.508079	+	0.861311i	$0.669644\pi$
$72$			23.3757i			2.75485i
$73$		−	11.7685i		−	1.37739i	−0.725050	−	0.688697i	$-0.758183\pi$
$73$		−	11.7685i		−	1.37739i	0.725050	−	0.688697i	$-0.241817\pi$
$74$	−10.0811			−1.17190
$75$	2.38787	+	0.294552i	0.275728	+	0.0340119i
$76$	8.63752			0.990791
$77$		−	2.96239i		−	0.337596i
$78$		0			0
$79$	2.26187			0.254480			0.127240	−	0.991872i	$-0.459388\pi$
$79$	2.26187			0.254480			0.127240	+	0.991872i	$0.459388\pi$
$80$	−20.5623	+	18.1817i	−2.29893	+	2.03278i
$81$	6.96968			0.774409
$82$		−	22.2374i		−	2.45571i
$83$			3.84367i			0.421898i	0.977497	+	0.210949i	$0.0676554\pi$
$83$			3.84367i			0.421898i	−0.977497	+	0.210949i	$0.932345\pi$
$84$	−2.00000			−0.218218
$85$	2.00000	+	2.26187i	0.216930	+	0.245334i
$86$	18.1744			1.95980
$87$		−	1.16362i		−	0.124753i
$88$			31.0313i			3.30794i
$89$	2.77575			0.294229			0.147114	−	0.989120i	$-0.453001\pi$
$89$	2.77575			0.294229			0.147114	+	0.989120i	$0.453001\pi$
$90$	10.9697	+	12.4060i	1.15631	+	1.30770i
$91$		0			0
$92$			33.4191i			3.48419i
$93$			2.54420i			0.263821i
$94$	−8.54420			−0.881267
$95$	2.80606	−	2.48119i	0.287896	−	0.254565i
$96$	7.67513			0.783340
$97$			1.87399i			0.190275i	0.995464	+	0.0951375i	$0.0303291\pi$
$97$			1.87399i			0.190275i	−0.995464	+	0.0951375i	$0.969671\pi$
$98$		−	16.9878i		−	1.71603i
$99$	10.1744			1.02257
$100$	−3.15633	+	25.5877i	−0.315633	+	2.55877i
$101$	10.4993			1.04472			0.522359	−	0.852725i	$-0.325052\pi$
$101$	10.4993			1.04472			0.522359	+	0.852725i	$0.325052\pi$
$102$		−	1.73813i		−	0.172101i
$103$		−	15.3684i		−	1.51429i	−0.653247	−	0.757145i	$-0.726594\pi$
$103$		−	15.3684i		−	1.51429i	0.653247	−	0.757145i	$-0.273406\pi$
$104$		0			0
$105$	−0.649738	+	0.574515i	−0.0634080	+	0.0560670i
$106$	−15.3503			−1.49095
$107$			11.1309i			1.07607i	0.842923	+	0.538034i	$0.180833\pi$
$107$			11.1309i			1.07607i	−0.842923	+	0.538034i	$0.819167\pi$
$108$		−	14.3127i		−	1.37724i
$109$	9.58769			0.918334			0.459167	−	0.888350i	$-0.348148\pi$
$109$	9.58769			0.918334			0.459167	+	0.888350i	$0.348148\pi$
$110$	14.5623	+	16.4690i	1.38846	+	1.57026i
$111$	1.81336			0.172116
$112$		−	9.89446i		−	0.934939i
$113$		−	0.574515i		−	0.0540459i	−0.999635	−	0.0270229i	$-0.991397\pi$
$113$		−	0.574515i		−	0.0540459i	0.999635	−	0.0270229i	$-0.00860271\pi$
$114$	−2.15633			−0.201958
$115$	9.59991	+	10.8568i	0.895196	+	1.01241i
$116$	12.4690			1.15772
$117$		0			0
$118$		−	16.0181i		−	1.47459i
$119$	−1.08840			−0.0997732
$120$	6.80606	−	6.01810i	0.621306	−	0.549375i
$121$	2.50659			0.227872
$122$			4.73084i			0.428310i
$123$			4.00000i			0.360668i
$124$	−27.2628			−2.44827
$125$	6.32487	+	9.21933i	0.565713	+	0.824602i
$126$	−5.96968			−0.531822
$127$		−	4.29455i		−	0.381080i	−0.981679	−	0.190540i	$-0.938976\pi$
$127$		−	4.29455i		−	0.381080i	0.981679	−	0.190540i	$-0.0610239\pi$
$128$			16.5696i			1.46456i
$129$	−3.26916			−0.287833
$130$		0			0
$131$	−0.836381			−0.0730749			−0.0365375	−	0.999332i	$-0.511633\pi$
$131$	−0.836381			−0.0730749			−0.0365375	+	0.999332i	$0.511633\pi$
$132$		−	9.11871i		−	0.793682i
$133$			1.35026i			0.117083i
$134$	−26.4690			−2.28657
$135$	−4.11142	−	4.64974i	−0.353855	−	0.400186i
$136$	11.4010			0.977632
$137$			14.9380i			1.27624i	0.769939	+	0.638118i	$0.220287\pi$
$137$			14.9380i			1.27624i	−0.769939	+	0.638118i	$0.779713\pi$
$138$		−	8.34297i		−	0.710201i
$139$	8.43866			0.715758			0.357879	−	0.933768i	$-0.383500\pi$
$139$	8.43866			0.715758			0.357879	+	0.933768i	$0.383500\pi$
$140$	−6.15633	−	6.96239i	−0.520304	−	0.588429i
$141$	1.53690			0.129431
$142$			22.9053i			1.92217i
$143$		0			0
$144$	33.9829			2.83190
$145$	4.05079	−	3.58181i	0.336399	−	0.297453i
$146$	−31.4821			−2.60548
$147$			3.05571i			0.252031i
$148$			19.4314i			1.59725i
$149$	−11.3503			−0.929850			−0.464925	−	0.885350i	$-0.653919\pi$
$149$	−11.3503			−0.929850			−0.464925	+	0.885350i	$0.653919\pi$
$150$	0.787965	−	6.38787i	0.0643371	−	0.521568i
$151$	−13.9878			−1.13831			−0.569155	−	0.822230i	$-0.692729\pi$
$151$	−13.9878			−1.13831			−0.569155	+	0.822230i	$0.692729\pi$
$152$		−	14.1441i		−	1.14724i
$153$		−	3.73813i		−	0.302210i
$154$	−7.92478			−0.638597
$155$	−8.85685	+	7.83146i	−0.711399	+	0.629038i
$156$		0			0
$157$			2.77575i			0.221529i	0.993847	+	0.110764i	$0.0353299\pi$
$157$			2.77575i			0.221529i	−0.993847	+	0.110764i	$0.964670\pi$
$158$		−	6.05079i		−	0.481375i
$159$	2.76116			0.218974
$160$	23.6253	+	26.7186i	1.86774	+	2.11229i
$161$	−5.22425			−0.411729
$162$		−	18.6448i		−	1.46487i
$163$			2.23155i			0.174788i	0.996174	+	0.0873942i	$0.0278540\pi$
$163$			2.23155i			0.174788i	−0.996174	+	0.0873942i	$0.972146\pi$
$164$	−42.8627			−3.34702
$165$	−2.61942	−	2.96239i	−0.203922	−	0.230622i
$166$	10.2823			0.798064
$167$			15.6932i			1.21438i	0.794557	+	0.607189i	$0.207703\pi$
$167$			15.6932i			1.21438i	−0.794557	+	0.607189i	$0.792297\pi$
$168$			3.27504i			0.252675i
$169$		0			0
$170$	6.05079	−	5.35026i	0.464074	−	0.410346i
$171$	−4.63752			−0.354640
$172$		−	35.0313i		−	2.67111i
$173$			25.5877i			1.94540i	0.232075	+	0.972698i	$0.425449\pi$
$173$			25.5877i			1.94540i	−0.232075	+	0.972698i	$0.574551\pi$
$174$	−3.11283			−0.235983
$175$	−4.00000	−	0.493413i	−0.302372	−	0.0372985i
$176$	45.1124			3.40047
$177$			2.88129i			0.216571i
$178$		−	7.42548i		−	0.556564i
$179$	−12.1260			−0.906340			−0.453170	−	0.891424i	$-0.649707\pi$
$179$	−12.1260			−0.906340			−0.453170	+	0.891424i	$0.649707\pi$
$180$	23.9126	−	21.1441i	1.78234	−	1.57599i
$181$	−2.73084			−0.202982			−0.101491	−	0.994836i	$-0.532361\pi$
$181$	−2.73084			−0.202982			−0.101491	+	0.994836i	$0.532361\pi$
$182$		0			0
$183$		−	0.850969i		−	0.0629054i
$184$	54.7245			4.03434
$185$	5.58181	+	6.31265i	0.410383	+	0.464115i
$186$	6.80606			0.499045
$187$		−	4.96239i		−	0.362886i
$188$			16.4690i			1.20112i
$189$	2.23743			0.162749
$190$	−6.63752	−	7.50659i	−0.481536	−	0.544585i
$191$	20.6253			1.49239			0.746197	−	0.665725i	$-0.231878\pi$
$191$	20.6253			1.49239			0.746197	+	0.665725i	$0.231878\pi$
$192$		−	8.71862i		−	0.629212i
$193$		−	21.7889i		−	1.56840i	−0.620508	−	0.784200i	$-0.713073\pi$
$193$		−	21.7889i		−	1.56840i	0.620508	−	0.784200i	$-0.286927\pi$
$194$	5.01317			0.359925
$195$		0			0
$196$	−32.7440			−2.33886
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		−	27.2179i		−	1.93429i
$199$	16.7513			1.18747			0.593734	−	0.804661i	$-0.297653\pi$
$199$	16.7513			1.18747			0.593734	+	0.804661i	$0.297653\pi$
$200$	41.9003	+	5.16854i	2.96280	+	0.365471i
$201$	4.76116			0.335826
$202$		−	28.0870i		−	1.97619i
$203$			1.94921i			0.136808i
$204$	−3.35026			−0.234565
$205$	−13.9248	+	12.3127i	−0.972549	+	0.859953i
$206$	−41.1124			−2.86443
$207$		−	17.9429i		−	1.24712i
$208$		0			0
$209$	−6.15633			−0.425842
$210$	1.53690	+	1.73813i	0.106056	+	0.119943i
$211$	−4.90175			−0.337451			−0.168725	−	0.985663i	$-0.553965\pi$
$211$	−4.90175			−0.337451			−0.168725	+	0.985663i	$0.553965\pi$
$212$			29.5877i			2.03209i
$213$		−	4.12013i		−	0.282307i
$214$	29.7767			2.03549
$215$	−10.0630	−	11.3806i	−0.686291	−	0.776149i
$216$	−23.4372			−1.59470
$217$		−	4.26187i		−	0.289314i
$218$		−	25.6483i		−	1.73712i
$219$	5.66291			0.382664
$220$	31.7440	−	28.0689i	2.14018	−	1.89240i
$221$		0			0
$222$		−	4.85097i		−	0.325576i
$223$			24.9076i			1.66794i	0.551811	+	0.833969i	$0.313937\pi$
$223$			24.9076i			1.66794i	−0.551811	+	0.833969i	$0.686063\pi$
$224$	−12.8568			−0.859034
$225$	1.69464	−	13.7381i	0.112976	−	0.915876i
$226$	−1.53690			−0.102233
$227$		−	9.95509i		−	0.660743i	−0.943851	−	0.330371i	$-0.892826\pi$
$227$		−	9.95509i		−	0.660743i	0.943851	−	0.330371i	$-0.107174\pi$
$228$			4.15633i			0.275259i
$229$	5.35026			0.353555			0.176778	−	0.984251i	$-0.443433\pi$
$229$	5.35026			0.353555			0.176778	+	0.984251i	$0.443433\pi$
$230$	29.0435	−	25.6810i	1.91507	−	1.69336i
$231$	1.42548			0.0937900
$232$		−	20.4182i		−	1.34052i
$233$			10.7612i			0.704987i	0.935814	+	0.352493i	$0.114666\pi$
$233$			10.7612i			0.704987i	−0.935814	+	0.352493i	$0.885334\pi$
$234$		0			0
$235$	4.73084	+	5.35026i	0.308606	+	0.349013i
$236$	−30.8749			−2.00979
$237$			1.08840i			0.0706990i
$238$			2.91160i			0.188731i
$239$	−11.8618			−0.767274			−0.383637	−	0.923484i	$-0.625329\pi$
$239$	−11.8618			−0.767274			−0.383637	+	0.923484i	$0.625329\pi$
$240$	−8.74894	−	9.89446i	−0.564742	−	0.638685i
$241$	28.6253			1.84392			0.921959	−	0.387288i	$-0.126588\pi$
$241$	28.6253			1.84392			0.921959	+	0.387288i	$0.126588\pi$
$242$		−	6.70545i		−	0.431043i
$243$			11.6810i			0.749337i
$244$	9.11871			0.583766
$245$	−10.6375	+	9.40597i	−0.679606	+	0.600925i
$246$	10.7005			0.682240
$247$		0			0
$248$			44.6434i			2.83486i
$249$	−1.84955			−0.117211
$250$	24.6629	−	16.9199i	1.55982	−	1.07011i
$251$	−19.3865			−1.22366			−0.611831	−	0.790988i	$-0.709567\pi$
$251$	−19.3865			−1.22366			−0.611831	+	0.790988i	$0.709567\pi$
$252$			11.5066i			0.724847i
$253$		−	23.8192i		−	1.49750i
$254$	−11.4885			−0.720852
$255$	−1.08840	+	0.962389i	−0.0681580	+	0.0602671i
$256$	8.08840			0.505525
$257$			22.8627i			1.42614i	0.701094	+	0.713069i	$0.252695\pi$
$257$			22.8627i			1.42614i	−0.701094	+	0.713069i	$0.747305\pi$
$258$			8.74543i			0.544467i
$259$	−3.03761			−0.188748
$260$		0			0
$261$	−6.69464			−0.414388
$262$			2.23743i			0.138229i
$263$		−	21.8822i		−	1.34932i	−0.738130	−	0.674658i	$-0.764291\pi$
$263$		−	21.8822i		−	1.34932i	0.738130	−	0.674658i	$-0.235709\pi$
$264$	−14.9321			−0.919005
$265$	8.49929	+	9.61213i	0.522107	+	0.590468i
$266$	3.61213			0.221474
$267$			1.33567i			0.0817419i
$268$			51.0191i			3.11648i
$269$	−22.7513			−1.38717			−0.693586	−	0.720374i	$-0.743970\pi$
$269$	−22.7513			−1.38717			−0.693586	+	0.720374i	$0.743970\pi$
$270$	−12.4387	+	10.9986i	−0.756993	+	0.669353i
$271$	−0.123638			−0.00751049			−0.00375525	−	0.999993i	$-0.501195\pi$
$271$	−0.123638			−0.00751049			−0.00375525	+	0.999993i	$0.501195\pi$
$272$		−	16.5745i		−	1.00498i
$273$		0			0
$274$	39.9610			2.41413
$275$	2.24965	−	18.2374i	0.135659	−	1.09976i
$276$	−16.0811			−0.967969
$277$		−	15.3503i		−	0.922308i	−0.887320	−	0.461154i	$-0.847436\pi$
$277$		−	15.3503i		−	0.922308i	0.887320	−	0.461154i	$-0.152564\pi$
$278$		−	22.5745i		−	1.35393i
$279$	14.6375			0.876325
$280$	−11.4010	+	10.0811i	−0.681343	+	0.602461i
$281$	−13.9248			−0.830683			−0.415341	−	0.909666i	$-0.636338\pi$
$281$	−13.9248			−0.830683			−0.415341	+	0.909666i	$0.636338\pi$
$282$		−	4.11142i		−	0.244831i
$283$		−	20.3815i		−	1.21156i	−0.795634	−	0.605778i	$-0.792862\pi$
$283$		−	20.3815i		−	1.21156i	0.795634	−	0.605778i	$-0.207138\pi$
$284$	44.1500			2.61982
$285$	1.19394	+	1.35026i	0.0707227	+	0.0799826i
$286$		0			0
$287$		−	6.70052i		−	0.395519i
$288$		−	44.1573i		−	2.60199i
$289$	15.1768			0.892753
$290$	−9.58181	−	10.8364i	−0.562663	−	0.636334i
$291$	−0.901754			−0.0528618
$292$			60.6820i			3.55114i
$293$			5.38058i			0.314337i	0.987572	+	0.157168i	$0.0502365\pi$
$293$			5.38058i			0.314337i	−0.987572	+	0.157168i	$0.949763\pi$
$294$	8.17442			0.476742
$295$	−10.0303	+	8.86907i	−0.583988	+	0.516377i
$296$	31.8192			1.84946
$297$			10.2012i			0.591935i
$298$			30.3634i			1.75891i
$299$		0			0
$300$	−12.3127	−	1.51881i	−0.710871	−	0.0876883i
$301$	5.47627			0.315647
$302$			37.4191i			2.15323i
$303$			5.05220i			0.290241i
$304$	−20.5623			−1.17933
$305$	2.96239	−	2.61942i	0.169626	−	0.149988i
$306$	−10.0000			−0.571662
$307$			19.1695i			1.09406i	0.837113	+	0.547031i	$0.184242\pi$
$307$			19.1695i			1.09406i	−0.837113	+	0.547031i	$0.815758\pi$
$308$			15.2750i			0.870376i
$309$	7.39517			0.420696
$310$	20.9502	+	23.6932i	1.18989	+	1.34568i
$311$	−25.2506			−1.43183			−0.715915	−	0.698187i	$-0.753990\pi$
$311$	−25.2506			−1.43183			−0.715915	+	0.698187i	$0.753990\pi$
$312$		0			0
$313$		−	2.81194i		−	0.158940i	−0.996837	−	0.0794702i	$-0.974677\pi$
$313$		−	2.81194i		−	0.158940i	0.996837	−	0.0794702i	$-0.0253229\pi$
$314$	7.42548			0.419044
$315$	3.30536	+	3.73813i	0.186236	+	0.210620i
$316$	−11.6629			−0.656090
$317$			23.7685i			1.33497i	0.744624	+	0.667485i	$0.232629\pi$
$317$			23.7685i			1.33497i	−0.744624	+	0.667485i	$0.767371\pi$
$318$		−	7.38646i		−	0.414212i
$319$	−8.88717			−0.497586
$320$	30.3512	−	26.8373i	1.69668	−	1.50025i
$321$	−5.35614			−0.298951
$322$			13.9756i			0.778828i
$323$			2.26187i			0.125854i
$324$	−35.9380			−1.99655
$325$		0			0
$326$	5.96968			0.330630
$327$			4.61354i			0.255129i
$328$			70.1886i			3.87551i
$329$	−2.57452			−0.141938
$330$	−7.92478	+	7.00729i	−0.436245	+	0.385739i
$331$	11.8011			0.648649			0.324325	−	0.945946i	$-0.394863\pi$
$331$	11.8011			0.648649			0.324325	+	0.945946i	$0.394863\pi$
$332$		−	19.8192i		−	1.08772i
$333$		−	10.4328i		−	0.571713i
$334$	41.9814			2.29712
$335$	14.6556	+	16.5745i	0.800722	+	0.905563i
$336$	4.76116			0.259742
$337$			16.1114i			0.877645i	0.898574	+	0.438822i	$0.144604\pi$
$337$			16.1114i			0.877645i	−0.898574	+	0.438822i	$0.855396\pi$
$338$		0			0
$339$	0.276454			0.0150149
$340$	−10.3127	−	11.6629i	−0.559282	−	0.632510i
$341$	19.4314			1.05227
$342$			12.4060i			0.670838i
$343$		−	10.7612i		−	0.581048i
$344$	−57.3644			−3.09288
$345$	−5.22425	+	4.61942i	−0.281264	+	0.248701i
$346$	68.4504			3.67992
$347$			27.4944i			1.47598i	0.674814	+	0.737988i	$0.264224\pi$
$347$			27.4944i			1.47598i	−0.674814	+	0.737988i	$0.735776\pi$
$348$			6.00000i			0.321634i
$349$	−17.6023			−0.942228			−0.471114	−	0.882072i	$-0.656148\pi$
$349$	−17.6023			−0.942228			−0.471114	+	0.882072i	$0.656148\pi$
$350$	−1.31994	+	10.7005i	−0.0705540	+	0.571967i
$351$		0			0
$352$		−	58.6190i		−	3.12440i
$353$			15.7685i			0.839270i	0.907693	+	0.419635i	$0.137842\pi$
$353$			15.7685i			0.839270i	−0.907693	+	0.419635i	$0.862158\pi$
$354$	7.70782			0.409666
$355$	14.3430	−	12.6824i	0.761246	−	0.673113i
$356$	−14.3127			−0.758569
$357$		−	0.523730i		−	0.0277187i
$358$			32.4387i			1.71444i
$359$	−14.8242			−0.782389			−0.391195	−	0.920308i	$-0.627938\pi$
$359$	−14.8242			−0.782389			−0.391195	+	0.920308i	$0.627938\pi$
$360$	−34.6239	−	39.1573i	−1.82484	−	2.06377i
$361$	−16.1939			−0.852312
$362$			7.30536i			0.383961i
$363$			1.20616i			0.0633067i
$364$		0			0
$365$	17.4314	+	19.7137i	0.912399	+	1.03186i
$366$	−2.27645			−0.118992
$367$		−	27.0313i		−	1.41102i	−0.708700	−	0.705510i	$-0.750718\pi$
$367$		−	27.0313i		−	1.41102i	0.708700	−	0.705510i	$-0.249282\pi$
$368$		−	79.5569i		−	4.14719i
$369$	23.0132			1.19802
$370$	16.8872	−	14.9321i	0.877922	−	0.776281i
$371$	−4.62530			−0.240134
$372$		−	13.1187i		−	0.680174i
$373$		−	12.9525i		−	0.670657i	−0.942101	−	0.335329i	$-0.891153\pi$
$373$		−	12.9525i		−	0.670657i	0.942101	−	0.335329i	$-0.108847\pi$
$374$	−13.2750			−0.686436
$375$	−4.43629	+	3.04349i	−0.229089	+	0.157165i
$376$	26.9683			1.39078
$377$		0			0
$378$		−	5.98541i		−	0.307856i
$379$	−30.2858			−1.55568			−0.777840	−	0.628463i	$-0.783684\pi$
$379$	−30.2858			−1.55568			−0.777840	+	0.628463i	$0.783684\pi$
$380$	−14.4690	+	12.7938i	−0.742243	+	0.656310i
$381$	2.06651			0.105871
$382$		−	55.1754i		−	2.82302i
$383$		−	21.0943i		−	1.07787i	−0.842348	−	0.538934i	$-0.818827\pi$
$383$		−	21.0943i		−	1.07787i	0.842348	−	0.538934i	$-0.181173\pi$
$384$	−7.97319			−0.406880
$385$	4.38787	+	4.96239i	0.223627	+	0.252907i
$386$	−58.2882			−2.96679
$387$			18.8084i			0.956086i
$388$		−	9.66291i		−	0.490560i
$389$	6.77575			0.343544			0.171772	−	0.985137i	$-0.445051\pi$
$389$	6.77575			0.343544			0.171772	+	0.985137i	$0.445051\pi$
$390$		0			0
$391$	−8.75131			−0.442573
$392$			53.6190i			2.70817i
$393$		−	0.402462i		−	0.0203015i
$394$	−5.35026			−0.269542
$395$	−3.78892	+	3.35026i	−0.190641	+	0.168570i
$396$	−52.4626			−2.63635
$397$		−	10.4690i		−	0.525423i	−0.964874	−	0.262711i	$-0.915383\pi$
$397$		−	10.4690i		−	0.525423i	0.964874	−	0.262711i	$-0.0846167\pi$
$398$		−	44.8119i		−	2.24622i
$399$	−0.649738			−0.0325276
$400$	7.51388	−	60.9135i	0.375694	−	3.04568i
$401$	−5.01317			−0.250346			−0.125173	−	0.992135i	$-0.539949\pi$
$401$	−5.01317			−0.250346			−0.125173	+	0.992135i	$0.539949\pi$
$402$		−	12.7367i		−	0.635250i
$403$		0			0
$404$	−54.1378			−2.69345
$405$	−11.6751	+	10.3235i	−0.580142	+	0.512977i
$406$	5.21440			0.258787
$407$		−	13.8496i		−	0.686497i
$408$			5.48612i			0.271603i
$409$	−14.3879			−0.711435			−0.355717	−	0.934594i	$-0.615763\pi$
$409$	−14.3879			−0.711435			−0.355717	+	0.934594i	$0.615763\pi$
$410$	32.9380	+	37.2506i	1.62669	+	1.83968i
$411$	−7.18806			−0.354561
$412$			79.2443i			3.90408i
$413$		−	4.82653i		−	0.237498i
$414$	−47.9995			−2.35905
$415$	−5.69323	−	6.43866i	−0.279470	−	0.316061i
$416$		0			0
$417$			4.06063i			0.198850i
$418$			16.4690i			0.805524i
$419$	−17.4617			−0.853059			−0.426529	−	0.904474i	$-0.640264\pi$
$419$	−17.4617			−0.853059			−0.426529	+	0.904474i	$0.640264\pi$
$420$	3.35026	−	2.96239i	0.163476	−	0.144550i
$421$	−2.88717			−0.140712			−0.0703559	−	0.997522i	$-0.522414\pi$
$421$	−2.88717			−0.140712			−0.0703559	+	0.997522i	$0.522414\pi$
$422$			13.1128i			0.638323i
$423$		−	8.84226i		−	0.429925i
$424$	48.4504			2.35296
$425$	−6.70052	−	0.826531i	−0.325023	−	0.0400927i
$426$	−11.0219			−0.534012
$427$			1.42548i			0.0689840i
$428$		−	57.3947i		−	2.77428i
$429$		0			0
$430$	−30.4445	+	26.9199i	−1.46817	+	1.29819i
$431$	−0.889535			−0.0428474			−0.0214237	−	0.999770i	$-0.506820\pi$
$431$	−0.889535			−0.0428474			−0.0214237	+	0.999770i	$0.506820\pi$
$432$			34.0724i			1.63931i
$433$			25.2506i			1.21347i	0.794906	+	0.606733i	$0.207520\pi$
$433$			25.2506i			1.21347i	−0.794906	+	0.606733i	$0.792480\pi$
$434$	−11.4010			−0.547268
$435$	1.72355	+	1.94921i	0.0826377	+	0.0934577i
$436$	−49.4372			−2.36761
$437$			10.8568i			0.519354i
$438$		−	15.1490i		−	0.723849i
$439$	−28.8119			−1.37512			−0.687560	−	0.726128i	$-0.741318\pi$
$439$	−28.8119			−1.37512			−0.687560	+	0.726128i	$0.741318\pi$
$440$	−45.9633	−	51.9814i	−2.19122	−	2.47812i
$441$	17.5804			0.837162
$442$		0			0
$443$		−	36.9805i		−	1.75700i	−0.477746	−	0.878498i	$-0.658546\pi$
$443$		−	36.9805i		−	1.75700i	0.477746	−	0.878498i	$-0.341454\pi$
$444$	−9.35026			−0.443744
$445$	−4.64974	+	4.11142i	−0.220419	+	0.194900i
$446$	66.6312			3.15508
$447$		−	5.46168i		−	0.258329i
$448$			14.6048i			0.690013i
$449$	−12.6859			−0.598686			−0.299343	−	0.954146i	$-0.596768\pi$
$449$	−12.6859			−0.598686			−0.299343	+	0.954146i	$0.596768\pi$
$450$	−36.7513	−	4.53339i	−1.73247	−	0.213706i
$451$	30.5501			1.43855
$452$			2.96239i			0.139339i
$453$		−	6.73084i		−	0.316242i
$454$	−26.6312			−1.24986
$455$		0			0
$456$	6.80606			0.318723
$457$			25.0494i			1.17176i	0.810398	+	0.585880i	$0.199251\pi$
$457$			25.0494i			1.17176i	−0.810398	+	0.585880i	$0.800749\pi$
$458$		−	14.3127i		−	0.668786i
$459$	3.74798			0.174941
$460$	−49.5002	−	55.9814i	−2.30796	−	2.61015i
$461$	36.8872			1.71801			0.859003	−	0.511970i	$-0.171084\pi$
$461$	36.8872			1.71801			0.859003	+	0.511970i	$0.171084\pi$
$462$		−	3.81336i		−	0.177413i
$463$		−	39.0191i		−	1.81337i	−0.421809	−	0.906685i	$-0.638605\pi$
$463$		−	39.0191i		−	1.81337i	0.421809	−	0.906685i	$-0.361395\pi$
$464$	−29.6834			−1.37802
$465$	−3.76845	−	4.26187i	−0.174758	−	0.197639i
$466$	28.7875			1.33356
$467$			32.7694i			1.51639i	0.652029	+	0.758194i	$0.273918\pi$
$467$			32.7694i			1.51639i	−0.652029	+	0.758194i	$0.726082\pi$
$468$		0			0
$469$	−7.97556			−0.368277
$470$	14.3127	−	12.6556i	0.660193	−	0.583760i
$471$	−1.33567			−0.0615446
$472$			50.5583i			2.32714i
$473$			24.9683i			1.14804i
$474$	2.91160			0.133734
$475$	−1.02539	+	8.31265i	−0.0470482	+	0.381411i
$476$	5.61213			0.257231
$477$		−	15.8858i		−	0.727359i
$478$			31.7318i			1.45138i
$479$	16.8749			0.771036			0.385518	−	0.922700i	$-0.374023\pi$
$479$	16.8749			0.771036			0.385518	+	0.922700i	$0.374023\pi$
$480$	−12.8568	+	11.3684i	−0.586832	+	0.518892i
$481$		0			0
$482$		−	76.5764i		−	3.48796i
$483$		−	2.51388i		−	0.114386i
$484$	−12.9248			−0.587490
$485$	−2.77575	−	3.13918i	−0.126040	−	0.142543i
$486$	31.2482			1.41745
$487$			9.24472i			0.418918i	0.977817	+	0.209459i	$0.0671703\pi$
$487$			9.24472i			0.418918i	−0.977817	+	0.209459i	$0.932830\pi$
$488$		−	14.9321i		−	0.675943i
$489$	−1.07381			−0.0485593
$490$	25.1622	+	28.4568i	1.13671	+	1.28555i
$491$	−25.7499			−1.16208			−0.581038	−	0.813876i	$-0.697353\pi$
$491$	−25.7499			−1.16208			−0.581038	+	0.813876i	$0.697353\pi$
$492$		−	20.6253i		−	0.929860i
$493$			3.26519i			0.147057i
$494$		0			0
$495$	−17.0435	+	15.0703i	−0.766048	+	0.677360i
$496$	64.9013			2.91415
$497$			6.90175i			0.309586i
$498$			4.94780i			0.221716i
$499$	−27.7015			−1.24009			−0.620044	−	0.784567i	$-0.712885\pi$
$499$	−27.7015			−1.24009			−0.620044	+	0.784567i	$0.712885\pi$
$500$	−32.6131	−	47.5379i	−1.45850	−	2.12596i
$501$	−7.55149			−0.337376
$502$			51.8613i			2.31468i
$503$		−	2.35519i		−	0.105013i	−0.998621	−	0.0525063i	$-0.983279\pi$
$503$		−	2.35519i		−	0.105013i	0.998621	−	0.0525063i	$-0.0167210\pi$
$504$	18.8423			0.839301
$505$	−17.5877	+	15.5515i	−0.782642	+	0.692032i
$506$	−63.7196			−2.83268
$507$		0			0
$508$			22.1441i			0.982486i
$509$	21.5125			0.953523			0.476762	−	0.879033i	$-0.341810\pi$
$509$	21.5125			0.953523			0.476762	+	0.879033i	$0.341810\pi$
$510$	2.57452	+	2.91160i	0.114001	+	0.128928i
$511$	−9.48612			−0.419641
$512$			11.5017i			0.508306i
$513$		−	4.64974i		−	0.205291i
$514$	61.1608			2.69769
$515$	22.7635	+	25.7440i	1.00308	+	1.13442i
$516$	16.8568			0.742081
$517$		−	11.7381i		−	0.516243i
$518$			8.12601i			0.357036i
$519$	−12.3127			−0.540465
$520$		0			0
$521$	37.7440			1.65360			0.826798	−	0.562499i	$-0.190160\pi$
$521$	37.7440			1.65360			0.826798	+	0.562499i	$0.190160\pi$
$522$			17.9090i			0.783858i
$523$		−	23.7416i		−	1.03815i	−0.854729	−	0.519075i	$-0.826277\pi$
$523$		−	23.7416i		−	1.03815i	0.854729	−	0.519075i	$-0.173723\pi$
$524$	4.31265			0.188399
$525$	0.237428	−	1.92478i	0.0103622	−	0.0840042i
$526$	−58.5379			−2.55237
$527$		−	7.13918i		−	0.310988i
$528$			21.7078i			0.944712i
$529$	−19.0059			−0.826343
$530$	25.7137	−	22.7367i	1.11693	−	0.987620i
$531$	16.5769			0.719376
$532$		−	6.96239i		−	0.301858i
$533$		0			0
$534$	3.57310			0.154623
$535$	−16.4871	−	18.6458i	−0.712798	−	0.806127i
$536$	83.5447			3.60858
$537$		−	5.83497i		−	0.251797i
$538$			60.8627i			2.62398i
$539$	23.3380			1.00524
$540$	21.1998	+	23.9756i	0.912295	+	1.03174i
$541$	−13.0376			−0.560531			−0.280265	−	0.959923i	$-0.590422\pi$
$541$	−13.0376			−0.560531			−0.280265	+	0.959923i	$0.590422\pi$
$542$			0.330749i			0.0142069i
$543$		−	1.31406i		−	0.0563919i
$544$	−21.5369			−0.923387
$545$	−16.0606	+	14.2012i	−0.687962	+	0.608314i
$546$		0			0
$547$			8.43041i			0.360458i	0.983625	+	0.180229i	$0.0576839\pi$
$547$			8.43041i			0.360458i	−0.983625	+	0.180229i	$0.942316\pi$
$548$		−	77.0249i		−	3.29034i
$549$	−4.89587			−0.208951
$550$	−48.7875	−	6.01810i	−2.08031	−	0.256613i
$551$	4.05079			0.172569
$552$			26.3331i			1.12081i
$553$		−	1.82321i		−	0.0775306i
$554$	−41.0640			−1.74464
$555$	−3.03761	+	2.68594i	−0.128939	+	0.114012i
$556$	−43.5125			−1.84534
$557$		−	13.6932i		−	0.580201i	−0.956996	−	0.290100i	$-0.906311\pi$
$557$		−	13.6932i		−	0.580201i	0.956996	−	0.290100i	$-0.0936887\pi$
$558$		−	39.1573i		−	1.65766i
$559$		0			0
$560$	14.6556	+	16.5745i	0.619313	+	0.700401i
$561$	2.38787			0.100816
$562$			37.2506i			1.57132i
$563$			8.86907i			0.373787i	0.982380	+	0.186893i	$0.0598419\pi$
$563$			8.86907i			0.373787i	−0.982380	+	0.186893i	$0.940158\pi$
$564$	−7.92478			−0.333693
$565$	0.850969	+	0.962389i	0.0358005	+	0.0404880i
$566$	−54.5233			−2.29178
$567$		−	5.61801i		−	0.235934i
$568$		−	72.2965i		−	3.03349i
$569$	32.7816			1.37428			0.687139	−	0.726526i	$-0.258866\pi$
$569$	32.7816			1.37428			0.687139	+	0.726526i	$0.258866\pi$
$570$	3.61213	−	3.19394i	0.151295	−	0.133779i
$571$	40.2882			1.68601			0.843005	−	0.537906i	$-0.180785\pi$
$571$	40.2882			1.68601			0.843005	+	0.537906i	$0.180785\pi$
$572$		0			0
$573$			9.92478i			0.414614i
$574$	−17.9248			−0.748166
$575$	−32.1622	−	3.96731i	−1.34126	−	0.165448i
$576$	−50.1608			−2.09003
$577$		−	28.8568i		−	1.20133i	−0.799502	−	0.600663i	$-0.794903\pi$
$577$		−	28.8568i		−	1.20133i	0.799502	−	0.600663i	$-0.205097\pi$
$578$		−	40.5999i		−	1.68873i
$579$	10.4847			0.435729
$580$	−20.8872	+	18.4690i	−0.867292	+	0.766882i
$581$	3.09825			0.128537
$582$			2.41231i			0.0999935i
$583$		−	21.0884i		−	0.873392i
$584$	99.3679			4.11187
$585$		0			0
$586$	14.3938			0.594600
$587$		−	41.6786i		−	1.72026i	−0.510074	−	0.860131i	$-0.670382\pi$
$587$		−	41.6786i		−	1.72026i	0.510074	−	0.860131i	$-0.329618\pi$
$588$		−	15.7562i		−	0.649776i
$589$	−8.85685			−0.364940
$590$	23.7259	+	26.8324i	0.976781	+	1.10467i
$591$	0.962389			0.0395874
$592$		−	46.2579i		−	1.90119i
$593$			22.4993i			0.923935i	0.886897	+	0.461968i	$0.152856\pi$
$593$			22.4993i			0.923935i	−0.886897	+	0.461968i	$0.847144\pi$
$594$	27.2896			1.11971
$595$	1.82321	−	1.61213i	0.0747442	−	0.0660908i
$596$	58.5256			2.39730
$597$			8.06063i			0.329900i
$598$		0			0
$599$	−4.15045			−0.169583			−0.0847913	−	0.996399i	$-0.527022\pi$
$599$	−4.15045			−0.169583			−0.0847913	+	0.996399i	$0.527022\pi$
$600$	−2.48707	+	20.1622i	−0.101534	+	0.823119i
$601$	27.9248			1.13908			0.569538	−	0.821965i	$-0.307122\pi$
$601$	27.9248			1.13908			0.569538	+	0.821965i	$0.307122\pi$
$602$		−	14.6497i		−	0.597079i
$603$		−	27.3923i		−	1.11550i
$604$	72.1255			2.93475
$605$	−4.19886	+	3.71274i	−0.170708	+	0.150944i
$606$	13.5153			0.549021
$607$			8.19489i			0.332620i	0.986073	+	0.166310i	$0.0531853\pi$
$607$			8.19489i			0.332620i	−0.986073	+	0.166310i	$0.946815\pi$
$608$			26.7186i			1.08358i
$609$	−0.937951			−0.0380077
$610$	−7.00729	−	7.92478i	−0.283717	−	0.320865i
$611$		0			0
$612$			19.2750i			0.779147i
$613$			33.1392i			1.33848i	0.743047	+	0.669239i	$0.233380\pi$
$613$			33.1392i			1.33848i	−0.743047	+	0.669239i	$0.766620\pi$
$614$	51.2809			2.06953
$615$	−5.92478	−	6.70052i	−0.238910	−	0.270191i
$616$	25.0132			1.00781
$617$			29.0132i			1.16803i	0.811744	+	0.584013i	$0.198518\pi$
$617$			29.0132i			1.16803i	−0.811744	+	0.584013i	$0.801482\pi$
$618$		−	19.7830i		−	0.795791i
$619$	12.2134			0.490900			0.245450	−	0.969409i	$-0.421064\pi$
$619$	12.2134			0.490900			0.245450	+	0.969409i	$0.421064\pi$
$620$	45.6688	−	40.3815i	1.83410	−	1.62176i
$621$	17.9902			0.721920
$622$			67.5487i			2.70845i
$623$		−	2.23743i		−	0.0896406i
$624$		0			0
$625$	−24.2506	−	6.07522i	−0.970024	−	0.243009i
$626$	−7.52232			−0.300652
$627$		−	2.96239i		−	0.118306i
$628$		−	14.3127i		−	0.571137i
$629$	−5.08840			−0.202888
$630$	10.0000	−	8.84226i	0.398410	−	0.352284i
$631$	1.22188			0.0486424			0.0243212	−	0.999704i	$-0.492258\pi$
$631$	1.22188			0.0486424			0.0243212	+	0.999704i	$0.492258\pi$
$632$			19.0982i			0.759687i
$633$		−	2.35870i		−	0.0937498i
$634$	63.5837			2.52523
$635$	6.36107	+	7.19394i	0.252431	+	0.285483i
$636$	−14.2374			−0.564551
$637$		0			0
$638$			23.7743i			0.941235i
$639$	−23.7043			−0.937728
$640$	−24.5428	−	27.7562i	−0.970139	−	1.09716i
$641$	−22.1016			−0.872960			−0.436480	−	0.899714i	$-0.643775\pi$
$641$	−22.1016			−0.872960			−0.436480	+	0.899714i	$0.643775\pi$
$642$			14.3284i			0.565496i
$643$			11.6688i			0.460172i	0.973170	+	0.230086i	$0.0739008\pi$
$643$			11.6688i			0.460172i	−0.973170	+	0.230086i	$0.926099\pi$
$644$	26.9380			1.06150
$645$	5.47627	−	4.84226i	0.215628	−	0.190664i
$646$	6.05079			0.238065
$647$			11.9575i			0.470096i	0.971984	+	0.235048i	$0.0755248\pi$
$647$			11.9575i			0.470096i	−0.971984	+	0.235048i	$0.924475\pi$
$648$			58.8491i			2.31181i
$649$	22.0059			0.863806
$650$		0			0
$651$	2.05079			0.0803766
$652$		−	11.5066i		−	0.450633i
$653$			10.9986i			0.430408i	0.976569	+	0.215204i	$0.0690416\pi$
$653$			10.9986i			0.430408i	−0.976569	+	0.215204i	$0.930958\pi$
$654$	12.3418			0.482604
$655$	1.40105	−	1.23884i	0.0547434	−	0.0484056i
$656$	102.038			3.98392
$657$		−	32.5804i		−	1.27108i
$658$			6.88717i			0.268490i
$659$	2.63989			0.102835			0.0514177	−	0.998677i	$-0.483626\pi$
$659$	2.63989			0.102835			0.0514177	+	0.998677i	$0.483626\pi$
$660$	13.5066	+	15.2750i	0.525743	+	0.594580i
$661$	−18.3028			−0.711896			−0.355948	−	0.934506i	$-0.615842\pi$
$661$	−18.3028			−0.711896			−0.355948	+	0.934506i	$0.615842\pi$
$662$		−	31.5696i		−	1.22699i
$663$		0			0
$664$	−32.4544			−1.25947
$665$	−2.00000	−	2.26187i	−0.0775567	−	0.0877114i
$666$	−27.9090			−1.08145
$667$			15.6728i			0.606852i
$668$		−	80.9194i		−	3.13087i
$669$	−11.9854			−0.463383
$670$	44.3390	−	39.2057i	1.71296	−	1.51465i
$671$	−6.49929			−0.250902
$672$		−	6.18664i		−	0.238655i
$673$		−	6.71037i		−	0.258666i	−0.991601	−	0.129333i	$-0.958716\pi$
$673$		−	6.71037i		−	0.258666i	0.991601	−	0.129333i	$-0.0412836\pi$
$674$	43.1002			1.66016
$675$	13.7743	+	1.69911i	0.530174	+	0.0653987i
$676$		0			0
$677$		−	1.57593i		−	0.0605679i	−0.999541	−	0.0302840i	$-0.990359\pi$
$677$		−	1.57593i		−	0.0605679i	0.999541	−	0.0302840i	$-0.00964116\pi$
$678$		−	0.739549i		−	0.0284022i
$679$	1.51056			0.0579698
$680$	−19.0982	+	16.8872i	−0.732384	+	0.647593i
$681$	4.79033			0.183566
$682$		−	51.9814i		−	1.99047i
$683$			15.1939i			0.581380i	0.956817	+	0.290690i	$0.0938848\pi$
$683$			15.1939i			0.581380i	−0.956817	+	0.290690i	$0.906115\pi$
$684$	23.9126			0.914320
$685$	−22.1260	−	25.0230i	−0.845391	−	0.956081i
$686$	−28.7875			−1.09911
$687$			2.57452i			0.0982239i
$688$			83.3947i			3.17939i
$689$		0			0
$690$	12.3576	+	13.9756i	0.470444	+	0.532041i
$691$	18.7127			0.711866			0.355933	−	0.934511i	$-0.384163\pi$
$691$	18.7127			0.711866			0.355933	+	0.934511i	$0.384163\pi$
$692$		−	131.938i		−	5.01555i
$693$		−	8.20123i		−	0.311539i
$694$	73.5510			2.79196
$695$	−14.1359	+	12.4993i	−0.536204	+	0.474125i
$696$	9.82512			0.372420
$697$		−	11.2243i		−	0.425149i
$698$			47.0884i			1.78232i
$699$	−5.17821			−0.195858
$700$	20.6253	+	2.54420i	0.779563	+	0.0961617i
$701$	24.3028			0.917904			0.458952	−	0.888461i	$-0.348225\pi$
$701$	24.3028			0.917904			0.458952	+	0.888461i	$0.348225\pi$
$702$		0			0
$703$			6.31265i			0.238086i
$704$	−66.5886			−2.50965
$705$	−2.57452	+	2.27645i	−0.0969619	+	0.0857362i
$706$	42.1827			1.58757
$707$		−	8.46310i		−	0.318287i
$708$		−	14.8568i		−	0.558355i
$709$	−9.66291			−0.362898			−0.181449	−	0.983400i	$-0.558079\pi$
$709$	−9.66291			−0.362898			−0.181449	+	0.983400i	$0.558079\pi$
$710$	−33.9271	−	38.3693i	−1.27326	−	1.43997i
$711$	6.26187			0.234838
$712$			23.4372i			0.878348i
$713$		−	34.2677i		−	1.28334i
$714$	−1.40105			−0.0524329
$715$		0			0
$716$	62.5256			2.33669
$717$		−	5.70782i		−	0.213162i
$718$			39.6566i			1.47997i
$719$	−28.4142			−1.05967			−0.529836	−	0.848100i	$-0.677746\pi$
$719$	−28.4142			−1.05967			−0.529836	+	0.848100i	$0.677746\pi$
$720$	−56.9257	+	50.3352i	−2.12150	+	1.87588i
$721$	−12.3879			−0.461349
$722$			43.3209i			1.61224i
$723$			13.7743i			0.512273i
$724$	14.0811			0.523320
$725$	−1.48024	+	12.0000i	−0.0549747	+	0.445669i
$726$	3.22662			0.119751
$727$		−	34.8545i		−	1.29268i	−0.763049	−	0.646341i	$-0.776299\pi$
$727$		−	34.8545i		−	1.29268i	0.763049	−	0.646341i	$-0.223701\pi$
$728$		0			0
$729$	15.2882			0.566230
$730$	52.7367	−	46.6312i	1.95187	−	1.72590i
$731$	9.17347			0.339293
$732$			4.38787i			0.162180i
$733$			6.25202i			0.230923i	0.993312	+	0.115462i	$0.0368348\pi$
$733$			6.25202i			0.230923i	−0.993312	+	0.115462i	$0.963165\pi$
$734$	−72.3122			−2.66909
$735$	−4.52610	−	5.11871i	−0.166948	−	0.188807i
$736$	−103.376			−3.81050
$737$		−	36.3634i		−	1.33946i
$738$		−	61.5633i		−	2.26617i
$739$	−32.0846			−1.18025			−0.590126	−	0.807311i	$-0.700922\pi$
$739$	−32.0846			−1.18025			−0.590126	+	0.807311i	$0.700922\pi$
$740$	−28.7816	−	32.5501i	−1.05803	−	1.19656i
$741$		0			0
$742$			12.3733i			0.454238i
$743$		−	30.5442i		−	1.12056i	−0.828304	−	0.560279i	$-0.810694\pi$
$743$		−	30.5442i		−	1.12056i	0.828304	−	0.560279i	$-0.189306\pi$
$744$	−21.4821			−0.787574
$745$	19.0132	−	16.8119i	0.696589	−	0.615942i
$746$	−34.6497			−1.26862
$747$			10.6410i			0.389335i
$748$			25.5877i			0.935579i
$749$	8.97224			0.327838
$750$	8.14174	+	11.8677i	0.297294	+	0.433345i
$751$	28.1622			1.02765			0.513827	−	0.857894i	$-0.328227\pi$
$751$	28.1622			1.02765			0.513827	+	0.857894i	$0.328227\pi$
$752$		−	39.2057i		−	1.42968i
$753$		−	9.32865i		−	0.339955i
$754$		0			0
$755$	23.4314	−	20.7186i	0.852755	−	0.754028i
$756$	−11.5369			−0.419593
$757$			35.4109i			1.28703i	0.765433	+	0.643515i	$0.222525\pi$
$757$			35.4109i			1.28703i	−0.765433	+	0.643515i	$0.777475\pi$
$758$			81.0186i			2.94273i
$759$	11.4617			0.416033
$760$	20.9502	+	23.6932i	0.759943	+	0.859444i
$761$	19.2388			0.697407			0.348704	−	0.937233i	$-0.386622\pi$
$761$	19.2388			0.697407			0.348704	+	0.937233i	$0.386622\pi$
$762$		−	5.52820i		−	0.200265i
$763$		−	7.72829i		−	0.279783i
$764$	−106.351			−3.84764
$765$	5.53690	+	6.26187i	0.200187	+	0.226398i
$766$	−56.4299			−2.03890
$767$		0			0
$768$			3.89209i			0.140444i
$769$	48.9643			1.76570			0.882849	−	0.469657i	$-0.155622\pi$
$769$	48.9643			1.76570			0.882849	+	0.469657i	$0.155622\pi$
$770$	13.2750	−	11.7381i	0.478399	−	0.423013i
$771$	−11.0014			−0.396206
$772$			112.351i			4.04359i
$773$			46.1681i			1.66055i	0.557354	+	0.830275i	$0.311817\pi$
$773$			46.1681i			1.66055i	−0.557354	+	0.830275i	$0.688183\pi$
$774$	50.3150			1.80854
$775$	3.23647	−	26.2374i	0.116258	−	0.942476i
$776$	−15.8232			−0.568020
$777$		−	1.46168i		−	0.0524375i
$778$		−	18.1260i		−	0.649849i
$779$	−13.9248			−0.498907
$780$		0			0
$781$	−31.4676			−1.12600
$782$			23.4109i			0.837172i
$783$		−	6.71228i		−	0.239877i
$784$	77.9497			2.78392
$785$	−4.11142	−	4.64974i	−0.146743	−	0.165956i
$786$	−1.07664			−0.0384024
$787$			22.6458i			0.807234i	0.914928	+	0.403617i	$0.132247\pi$
$787$			22.6458i			0.807234i	−0.914928	+	0.403617i	$0.867753\pi$
$788$			10.3127i			0.367373i
$789$	10.5296			0.374864
$790$	8.96239	+	10.1359i	0.318867	+	0.360618i
$791$	−0.463096			−0.0164658
$792$			85.9086i			3.05263i
$793$		0			0
$794$	−28.0059			−0.993891
$795$	−4.62530	+	4.08981i	−0.164043	+	0.145051i
$796$	−86.3752			−3.06149
$797$			8.23743i			0.291785i	0.989300	+	0.145892i	$0.0466053\pi$
$797$			8.23743i			0.291785i	−0.989300	+	0.145892i	$0.953395\pi$
$798$			1.73813i			0.0615293i
$799$	−4.31265			−0.152571
$800$	−79.1509	−	9.76353i	−2.79841	−	0.345193i
$801$	7.68452			0.271519
$802$			13.4109i			0.473555i
$803$		−	43.2506i		−	1.52628i
$804$	−24.5501			−0.865814
$805$	8.75131	−	7.73813i	0.308443	−	0.272733i
$806$		0			0
$807$		−	10.9478i		−	0.385381i
$808$			88.6516i			3.11875i
$809$	−44.1319			−1.55159			−0.775797	−	0.630982i	$-0.782652\pi$
$809$	−44.1319			−1.55159			−0.775797	+	0.630982i	$0.782652\pi$
$810$	27.6166	+	31.2325i	0.970348	+	1.09740i
$811$	−22.6883			−0.796694			−0.398347	−	0.917235i	$-0.630416\pi$
$811$	−22.6883			−0.796694			−0.398347	+	0.917235i	$0.630416\pi$
$812$		−	10.0508i		−	0.352713i
$813$		−	0.0594941i		−	0.00208655i
$814$	−37.0494			−1.29858
$815$	−3.30536	−	3.73813i	−0.115782	−	0.130941i
$816$	7.97556			0.279201
$817$		−	11.3806i		−	0.398156i
$818$			38.4894i			1.34575i
$819$		0			0
$820$	71.8007	−	63.4880i	2.50739	−	2.21710i
$821$	50.2736			1.75456			0.877281	−	0.479978i	$-0.159355\pi$
$821$	50.2736			1.75456			0.877281	+	0.479978i	$0.159355\pi$
$822$			19.2290i			0.670688i
$823$		−	5.13093i		−	0.178853i	−0.995993	−	0.0894265i	$-0.971497\pi$
$823$		−	5.13093i		−	0.178853i	0.995993	−	0.0894265i	$-0.0285034\pi$
$824$	129.764			4.52054
$825$	8.77575	+	1.08252i	0.305532	+	0.0376884i
$826$	−12.9116			−0.449252
$827$		−	18.6946i		−	0.650076i	−0.945701	−	0.325038i	$-0.894623\pi$
$827$		−	18.6946i		−	0.650076i	0.945701	−	0.325038i	$-0.105377\pi$
$828$			92.5193i			3.21527i
$829$	3.44121			0.119518			0.0597591	−	0.998213i	$-0.480967\pi$
$829$	3.44121			0.119518			0.0597591	+	0.998213i	$0.480967\pi$
$830$	−17.2243	+	15.2301i	−0.597863	+	0.528646i
$831$	7.38646			0.256233
$832$		0			0
$833$		−	8.57452i		−	0.297089i
$834$	10.8627			0.376146
$835$	−23.2447	−	26.2882i	−0.804417	−	0.909741i
$836$	31.7440			1.09789
$837$			14.6761i			0.507280i
$838$			46.7123i			1.61365i
$839$	−52.6248			−1.81681			−0.908406	−	0.418090i	$-0.862700\pi$
$839$	−52.6248			−1.81681			−0.908406	+	0.418090i	$0.862700\pi$
$840$	−4.85097	−	5.48612i	−0.167374	−	0.189289i
$841$	−23.1524			−0.798357
$842$			7.72355i			0.266171i
$843$		−	6.70052i		−	0.230778i
$844$	25.2750			0.870003
$845$		0			0
$846$	−23.6542			−0.813248
$847$		−	2.02047i		−	0.0694241i
$848$		−	70.4358i		−	2.41878i
$849$	9.80748			0.336592
$850$	−2.21108	+	17.9248i	−0.0758394	+	0.614815i
$851$	−24.4241			−0.837246
$852$			21.2447i			0.727832i
$853$		−	6.31853i		−	0.216342i	−0.994132	−	0.108171i	$-0.965501\pi$
$853$		−	6.31853i		−	0.216342i	0.994132	−	0.108171i	$-0.0344995\pi$
$854$	3.81336			0.130490
$855$	7.76845	−	6.86907i	0.265675	−	0.234917i
$856$	−93.9850			−3.21234
$857$		−	0.775746i		−	0.0264990i	−0.999912	−	0.0132495i	$-0.995782\pi$
$857$		−	0.775746i		−	0.0264990i	0.999912	−	0.0132495i	$-0.00421757\pi$
$858$		0			0
$859$	−3.24869			−0.110844			−0.0554220	−	0.998463i	$-0.517650\pi$
$859$	−3.24869			−0.110844			−0.0554220	+	0.998463i	$0.517650\pi$
$860$	51.8881	+	58.6820i	1.76937	+	2.00104i
$861$	3.22425			0.109882
$862$			2.37962i			0.0810503i
$863$		−	19.9208i		−	0.678112i	−0.940766	−	0.339056i	$-0.889892\pi$
$863$		−	19.9208i		−	0.678112i	0.940766	−	0.339056i	$-0.110108\pi$
$864$	44.2736			1.50622
$865$	−37.9003	−	42.8627i	−1.28865	−	1.45738i
$866$	67.5487			2.29540
$867$			7.30299i			0.248022i
$868$			21.9756i			0.745899i
$869$	8.31265			0.281987
$870$	5.21440	−	4.61071i	0.176785	−	0.156318i
$871$		0			0
$872$			80.9544i			2.74146i
$873$			5.18806i			0.175589i
$874$	29.0435			0.982411
$875$	7.43136	−	5.09825i	0.251226	−	0.172352i
$876$	−29.1998			−0.986570
$877$		−	22.1378i		−	0.747539i	−0.927522	−	0.373770i	$-0.878065\pi$
$877$		−	22.1378i		−	0.747539i	0.927522	−	0.373770i	$-0.121935\pi$
$878$			77.0757i			2.60118i
$879$	−2.58910			−0.0873283
$880$	−75.5691	+	66.8202i	−2.54743	+	2.25251i
$881$	2.23155			0.0751828			0.0375914	−	0.999293i	$-0.488031\pi$
$881$	2.23155			0.0751828			0.0375914	+	0.999293i	$0.488031\pi$
$882$		−	47.0299i		−	1.58358i
$883$			4.30440i			0.144855i	0.997374	+	0.0724273i	$0.0230745\pi$
$883$			4.30440i			0.144855i	−0.997374	+	0.0724273i	$0.976925\pi$
$884$		0			0
$885$	−4.26774	−	4.82653i	−0.143459	−	0.162242i
$886$	−98.9276			−3.32354
$887$			15.9330i			0.534979i	0.963561	+	0.267489i	$0.0861940\pi$
$887$			15.9330i			0.534979i	−0.963561	+	0.267489i	$0.913806\pi$
$888$			15.3112i			0.513811i
$889$	−3.46168			−0.116101
$890$	10.9986	+	12.4387i	0.368673	+	0.416945i
$891$	25.6145			0.858118
$892$		−	128.432i		−	4.30022i
$893$			5.35026i			0.179040i
$894$	−14.6107			−0.488655
$895$	20.3127	−	17.9610i	0.678977	−	0.600369i
$896$	13.3561			0.446197
$897$		0			0
$898$			33.9365i			1.13248i
$899$	−12.7856			−0.426423
$900$	−8.73813	+	70.8383i	−0.291271	+	2.36128i
$901$	−7.74798			−0.258123
$902$		−	81.7255i		−	2.72116i
$903$			2.63515i			0.0876923i
$904$	4.85097			0.161341
$905$	4.57452	−	4.04491i	0.152062	−	0.134457i
$906$	−18.0059			−0.598205
$907$		−	51.9086i		−	1.72360i	−0.507251	−	0.861798i	$-0.669338\pi$
$907$		−	51.9086i		−	1.72360i	0.507251	−	0.861798i	$-0.330662\pi$
$908$			51.3317i			1.70350i
$909$	29.0668			0.964085
$910$		0			0
$911$	−9.67750			−0.320630			−0.160315	−	0.987066i	$-0.551251\pi$
$911$	−9.67750			−0.320630			−0.160315	+	0.987066i	$0.551251\pi$
$912$		−	9.89446i		−	0.327638i
$913$			14.1260i			0.467503i
$914$	67.0103			2.21651
$915$	1.26045	+	1.42548i	0.0416692	+	0.0471251i
$916$	−27.5877			−0.911523
$917$			0.674176i			0.0222632i
$918$		−	10.0263i		−	0.330919i
$919$	−13.5515			−0.447022			−0.223511	−	0.974701i	$-0.571752\pi$
$919$	−13.5515			−0.447022			−0.223511	+	0.974701i	$0.571752\pi$
$920$	−91.6707	+	81.0576i	−3.02229	+	2.67239i
$921$	−9.22425			−0.303949
$922$		−	98.6780i		−	3.24979i
$923$		0			0
$924$	−7.35026			−0.241806
$925$	−18.7005	−	2.30677i	−0.614869	−	0.0758462i
$926$	−104.381			−3.43017
$927$		−	42.5466i		−	1.39741i
$928$			38.5705i			1.26614i
$929$	−9.44992			−0.310042			−0.155021	−	0.987911i	$-0.549545\pi$
$929$	−9.44992			−0.310042			−0.155021	+	0.987911i	$0.549545\pi$
$930$	−11.4010	+	10.0811i	−0.373855	+	0.330572i
$931$	−10.6375			−0.348631
$932$		−	55.4880i		−	1.81757i
$933$		−	12.1504i		−	0.397788i
$934$	87.6625			2.86840
$935$	7.35026	+	8.31265i	0.240379	+	0.271853i
$936$		0			0
$937$			16.0409i			0.524035i	0.965063	+	0.262017i	$0.0843877\pi$
$937$			16.0409i			0.524035i	−0.965063	+	0.262017i	$0.915612\pi$
$938$			21.3357i			0.696634i
$939$	1.35309			0.0441565
$940$	−24.3938	−	27.5877i	−0.795636	−	0.899811i
$941$	21.6747			0.706574			0.353287	−	0.935515i	$-0.385064\pi$
$941$	21.6747			0.706574			0.353287	+	0.935515i	$0.385064\pi$
$942$			3.57310i			0.116418i
$943$		−	53.8759i		−	1.75444i
$944$	73.5002			2.39223
$945$	−3.74798	+	3.31406i	−0.121922	+	0.107807i
$946$	66.7934			2.17164
$947$			4.63118i			0.150493i	0.997165	+	0.0752466i	$0.0239744\pi$
$947$			4.63118i			0.150493i	−0.997165	+	0.0752466i	$0.976026\pi$
$948$		−	5.61213i		−	0.182273i
$949$		0			0
$950$	22.2374	+	2.74306i	0.721477	+	0.0889966i
$951$	−11.4372			−0.370878
$952$		−	9.18997i		−	0.297849i
$953$		−	26.2981i		−	0.851878i	−0.904752	−	0.425939i	$-0.859944\pi$
$953$		−	26.2981i		−	0.851878i	0.904752	−	0.425939i	$-0.140056\pi$
$954$	−42.4965			−1.37587
$955$	−34.5501	+	30.5501i	−1.11801	+	0.988577i
$956$	61.1632			1.97816
$957$		−	4.27645i		−	0.138238i
$958$		−	45.1427i		−	1.45849i
$959$	12.0409			0.388822
$960$	12.9140	+	14.6048i	0.416797	+	0.471369i
$961$	−3.04491			−0.0982228
$962$		0			0
$963$			30.8155i			0.993014i
$964$	−147.601			−4.75392
$965$	32.2736	+	36.4993i	1.03892	+	1.17495i
$966$	−6.72496			−0.216372
$967$			11.9405i			0.383981i	0.981397	+	0.191990i	$0.0614942\pi$
$967$			11.9405i			0.383981i	−0.981397	+	0.191990i	$0.938506\pi$
$968$			21.1646i			0.680255i
$969$	−1.08840			−0.0349643
$970$	−8.39772	+	7.42548i	−0.269635	+	0.238418i
$971$	30.1524			0.967635			0.483818	−	0.875169i	$-0.339250\pi$
$971$	30.1524			0.967635			0.483818	+	0.875169i	$0.339250\pi$
$972$		−	60.2311i		−	1.93191i
$973$		−	6.80209i		−	0.218065i
$974$	24.7308			0.792427
$975$		0			0
$976$	−21.7078			−0.694850
$977$		−	26.9321i		−	0.861633i	−0.902439	−	0.430817i	$-0.858226\pi$
$977$		−	26.9321i		−	0.861633i	0.902439	−	0.430817i	$-0.141774\pi$
$978$			2.87258i			0.0918549i
$979$	10.2012			0.326033
$980$	54.8505	−	48.5002i	1.75214	−	1.54928i
$981$	26.5431			0.847455
$982$			68.8843i			2.19819i
$983$		−	20.5902i		−	0.656727i	−0.944551	−	0.328363i	$-0.893503\pi$
$983$		−	20.5902i		−	0.656727i	0.944551	−	0.328363i	$-0.106497\pi$
$984$	−33.7743			−1.07669
$985$	2.96239	+	3.35026i	0.0943895	+	0.106748i
$986$	8.73481			0.278173
$987$		−	1.23884i		−	0.0394328i
$988$		0			0
$989$	44.0322			1.40014
$990$	40.3150	+	45.5936i	1.28130	+	1.44906i
$991$	−48.1378			−1.52915			−0.764573	−	0.644537i	$-0.777050\pi$
$991$	−48.1378			−1.52915			−0.764573	+	0.644537i	$0.777050\pi$
$992$		−	84.3327i		−	2.67756i
$993$			5.67864i			0.180206i
$994$	18.4631			0.585614
$995$	−28.0606	+	24.8119i	−0.889582	+	0.786591i
$996$	9.53690			0.302188
$997$			33.4255i			1.05860i	0.848436	+	0.529298i	$0.177545\pi$
$997$			33.4255i			1.05860i	−0.848436	+	0.529298i	$0.822455\pi$
$998$			74.1051i			2.34576i
$999$	10.4603			0.330948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.b.c.339.1		6
5.2	odd	4		4225.2.a.bh.1.3		3
5.3	odd	4		4225.2.a.ba.1.1		3
5.4	even	2	inner	845.2.b.c.339.6		6
13.2	odd	12		845.2.l.e.654.5		12
13.3	even	3		845.2.n.g.529.6		12
13.4	even	6		845.2.n.f.484.6		12
13.5	odd	4		845.2.d.a.844.2		6
13.6	odd	12		845.2.l.e.699.6		12
13.7	odd	12		845.2.l.d.699.2		12
13.8	odd	4		845.2.d.b.844.6		6
13.9	even	3		845.2.n.g.484.1		12
13.10	even	6		845.2.n.f.529.1		12
13.11	odd	12		845.2.l.d.654.1		12
13.12	even	2		65.2.b.a.14.6	yes	6
39.38	odd	2		585.2.c.b.469.1		6
52.51	odd	2		1040.2.d.c.209.3		6
65.4	even	6		845.2.n.f.484.1		12
65.9	even	6		845.2.n.g.484.6		12
65.12	odd	4		325.2.a.j.1.1		3
65.19	odd	12		845.2.l.d.699.1		12
65.24	odd	12		845.2.l.e.654.6		12
65.29	even	6		845.2.n.g.529.1		12
65.34	odd	4		845.2.d.a.844.1		6
65.38	odd	4		325.2.a.k.1.3		3
65.44	odd	4		845.2.d.b.844.5		6
65.49	even	6		845.2.n.f.529.6		12
65.54	odd	12		845.2.l.d.654.2		12
65.59	odd	12		845.2.l.e.699.5		12
65.64	even	2		65.2.b.a.14.1	✓	6
195.38	even	4		2925.2.a.bf.1.1		3
195.77	even	4		2925.2.a.bj.1.3		3
195.194	odd	2		585.2.c.b.469.6		6
260.103	even	4		5200.2.a.cb.1.3		3
260.207	even	4		5200.2.a.cj.1.1		3
260.259	odd	2		1040.2.d.c.209.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.1	✓	6	65.64	even	2
65.2.b.a.14.6	yes	6	13.12	even	2
325.2.a.j.1.1		3	65.12	odd	4
325.2.a.k.1.3		3	65.38	odd	4
585.2.c.b.469.1		6	39.38	odd	2
585.2.c.b.469.6		6	195.194	odd	2
845.2.b.c.339.1		6	1.1	even	1	trivial
845.2.b.c.339.6		6	5.4	even	2	inner
845.2.d.a.844.1		6	65.34	odd	4
845.2.d.a.844.2		6	13.5	odd	4
845.2.d.b.844.5		6	65.44	odd	4
845.2.d.b.844.6		6	13.8	odd	4
845.2.l.d.654.1		12	13.11	odd	12
845.2.l.d.654.2		12	65.54	odd	12
845.2.l.d.699.1		12	65.19	odd	12
845.2.l.d.699.2		12	13.7	odd	12
845.2.l.e.654.5		12	13.2	odd	12
845.2.l.e.654.6		12	65.24	odd	12
845.2.l.e.699.5		12	65.59	odd	12
845.2.l.e.699.6		12	13.6	odd	12
845.2.n.f.484.1		12	65.4	even	6
845.2.n.f.484.6		12	13.4	even	6
845.2.n.f.529.1		12	13.10	even	6
845.2.n.f.529.6		12	65.49	even	6
845.2.n.g.484.1		12	13.9	even	3
845.2.n.g.484.6		12	65.9	even	6
845.2.n.g.529.1		12	65.29	even	6
845.2.n.g.529.6		12	13.3	even	3
1040.2.d.c.209.3		6	52.51	odd	2
1040.2.d.c.209.4		6	260.259	odd	2
2925.2.a.bf.1.1		3	195.38	even	4
2925.2.a.bj.1.3		3	195.77	even	4
4225.2.a.ba.1.1		3	5.3	odd	4
4225.2.a.bh.1.3		3	5.2	odd	4
5200.2.a.cb.1.3		3	260.103	even	4
5200.2.a.cj.1.1		3	260.207	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.67513i q^{2} +0.481194i q^{3} -5.15633 q^{4} +(-1.67513 + 1.48119i) q^{5} +1.28726 q^{6} -0.806063i q^{7} +8.44358i q^{8} +2.76845 q^{9} +(3.96239 + 4.48119i) q^{10} +3.67513 q^{11} -2.48119i q^{12} -2.15633 q^{14} +(-0.712742 - 0.806063i) q^{15} +12.2750 q^{16} -1.35026i q^{17} -7.40597i q^{18} -1.67513 q^{19} +(8.63752 - 7.63752i) q^{20} +0.387873 q^{21} -9.83146i q^{22} -6.48119i q^{23} -4.06300 q^{24} +(0.612127 - 4.96239i) q^{25} +2.77575i q^{27} +4.15633i q^{28} -2.41819 q^{29} +(-2.15633 + 1.90668i) q^{30} +5.28726 q^{31} -15.9502i q^{32} +1.76845i q^{33} -3.61213 q^{34} +(1.19394 + 1.35026i) q^{35} -14.2750 q^{36} -3.76845i q^{37} +4.48119i q^{38} +(-12.5066 - 14.1441i) q^{40} +8.31265 q^{41} -1.03761i q^{42} +6.79384i q^{43} -18.9502 q^{44} +(-4.63752 + 4.10062i) q^{45} -17.3380 q^{46} -3.19394i q^{47} +5.90668i q^{48} +6.35026 q^{49} +(-13.2750 - 1.63752i) q^{50} +0.649738 q^{51} -5.73813i q^{53} +7.42548 q^{54} +(-6.15633 + 5.44358i) q^{55} +6.80606 q^{56} -0.806063i q^{57} +6.46898i q^{58} +5.98778 q^{59} +(3.67513 + 4.15633i) q^{60} -1.76845 q^{61} -14.1441i q^{62} -2.23155i q^{63} -18.1187 q^{64} +4.73084 q^{66} -9.89446i q^{67} +6.96239i q^{68} +3.11871 q^{69} +(3.61213 - 3.19394i) q^{70} -8.56230 q^{71} +23.3757i q^{72} -11.7685i q^{73} -10.0811 q^{74} +(2.38787 + 0.294552i) q^{75} +8.63752 q^{76} -2.96239i q^{77} +2.26187 q^{79} +(-20.5623 + 18.1817i) q^{80} +6.96968 q^{81} -22.2374i q^{82} +3.84367i q^{83} -2.00000 q^{84} +(2.00000 + 2.26187i) q^{85} +18.1744 q^{86} -1.16362i q^{87} +31.0313i q^{88} +2.77575 q^{89} +(10.9697 + 12.4060i) q^{90} +33.4191i q^{92} +2.54420i q^{93} -8.54420 q^{94} +(2.80606 - 2.48119i) q^{95} +7.67513 q^{96} +1.87399i q^{97} -16.9878i q^{98} +10.1744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} - 4 q^{6} - 6 q^{9} + 2 q^{10} + 12 q^{11} + 8 q^{14} - 16 q^{15} + 10 q^{16} + 20 q^{20} + 4 q^{21} - 16 q^{24} + 2 q^{25} - 12 q^{29} + 8 q^{30} + 20 q^{31} - 20 q^{34} + 8 q^{35} - 22 q^{36}+ \cdots - 16 q^{99}+O(q^{100}) \) 6 * q - 10 * q^4 - 4 * q^6 - 6 * q^9 + 2 * q^10 + 12 * q^11 + 8 * q^14 - 16 * q^15 + 10 * q^16 + 20 * q^20 + 4 * q^21 - 16 * q^24 + 2 * q^25 - 12 * q^29 + 8 * q^30 + 20 * q^31 - 20 * q^34 + 8 * q^35 - 22 * q^36 - 34 * q^40 + 8 * q^41 - 40 * q^44 + 4 * q^45 - 32 * q^46 + 18 * q^49 - 16 * q^50 + 24 * q^51 + 68 * q^54 - 16 * q^55 + 40 * q^56 - 16 * q^59 + 12 * q^60 + 12 * q^61 - 66 * q^64 - 16 * q^66 - 24 * q^69 + 20 * q^70 + 24 * q^71 + 4 * q^74 + 16 * q^75 + 20 * q^76 + 32 * q^79 - 48 * q^80 + 46 * q^81 - 12 * q^84 + 12 * q^85 + 32 * q^86 + 20 * q^89 + 70 * q^90 - 32 * q^94 + 16 * q^95 + 36 * q^96 - 16 * q^99

Introduction

L-functions

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